According to Hooke's Law, the force required to hold the spring stretched x m beyond its natural length is given by f(x) = kx,
where k is the spring constant.
Suppose that 3 J of work is needed to stretch a spring from 9 cm to 11 cm and another 5 J is needed to stretch it from 11 cm to 13 cm. Find the exact value of k, in N/m.

Suppose there is a simple index of three stocks, stock abc, stock xyz, and stock qrs. stock abc opens on day 1 with 4000 shares at $3.15 per share. stock xyz opens on day 1 with 5000 shares at $4.30 per share. stock qrs opens on day 1 with 6000 shares at $4.60 per share. the price of stock abc on day 8 begins at $3.50. the price of stock xyz on day 8 begins at $3.90. stock qrs opens on day 8 with a price of $4.50 per share. assume that each stock has the same number of shares that it opened with on day 1. what is the rate of change of this simple index over 1 week?

Prove that the value of the expression 7^8–7^7+7^6 is divisible by 43.

How can constraints be used to model a real-world situation?